A Type Calculus for Executable Modelling Languages

There is considerable current interest in the design and constructionof directly executable modelling languages for mathematicalprogramming. The present research extends contemporary modellinglanguages by specifying a type calculus for an extended dimensionalsystem that determines if the model is well formed in the sensethat the objective function and constraints consist of homogeneouscomponents. Each variable, coefficient, constant, function,constraint, input, and output of the model is assigned a typethat consists of its concepts, quantities, and units of measurementwith optional scale factors. In checking the composition offunctions and constraints, the system can do automatic unitconversions and apply user-supplied conversions. The systemallows a hierarchy of concepts that provides inheritance ofquantities and automatic concept conversion. In addition, eachset in a model is typed so the system can check the validityof operations on indices.     

The flat-maximum effect and generic linear scoring models: a test

Received on 1 July 1991. Predicting human behaviour patterns with linear correlationmodels has absorbed researchers for the past five decades. Althoughmost observers generally concede that humans are inferior tosuch models in combining information, linear scoring modelsare unfortunately, plagued by the flat-maximum effect or the‘curse of insensitivity’. As Lovie & Lovie(1986)observe: ‘The predictive ability of linear models is insensitiveto large variations in the size of regression weights and tothe number of predictors.’ In essence, seemingly differentscoringmodels tend to produce indistinguishable predictive outcomes. Since its demonstration by Dawes & Corrigan (1974), observershave cast the flat maximum in a decidedly negative light. Incontrast, Lovie & Lovie (1986) present a provocatively contrarianview of the flat maximum‘s positive potential. In thissame vein, we examine the predictive power of a generic credit-scoringmodel versus individual empirically derived systems. If, asWainer (1976) noted in regard to the flat maximum, ’itdon‘t make no nevermind’, generic credit-scoringmodels could provide cheaper alternatives to individual empiricallyderived models. During the period 1984–8, a series of linear credit-scoringmodels were developed for ten Southeastern U.S. credit unions.For each credit union, stepwise multiple regression was employedto select a subset of explanatory variables to be used in adiscriminant analysis. A generic credit-scoring equation wasdeveloped from the resulting discriminant analyses using weightedaverage coefficients from five systems. The predictive powerof the generic model was compared to the predictive power ofholdout sample of the five remaining credit-scoring models. In all cases, the generic model's performance was very closeto that of the empirically derived models. Thus, our findingssupport Lovie & Lovie's (1986) challenge to the conventionalwisdom that the flat maximum casts a pall on the successfulmodelling of judgement processes. Indeed, the flat maximum impliesa positive role for simpler, and hence cheaper, generic models.Although further research is needed, it should be possible todevelop hybrid models with generic cores that perform as wellas empirically derived linear models.     

Theoretical investigation of the transition states leading to HCI elimination in 2-chloropropene

This paper describes ab initio electronic structure calculations on the planar transition states of 2-chloropropene leading to HCI elimination in the ground electronic state to form either propyne or allene as the cofragment. The calculations provide optimized geometries of the transition states for these two reaction channels, together with vibrational frequencies, barrier heights, and reaction endothermicities. The calculated barrier heights for the two distinct four-centre HCI elimination transition states, one leading to HCI and propyne and the other leading to HCI and allene, are 72.5kcalmol^?1 (77.8kcalmol^?1 without zero-point correction) and 73.2kcalmol^?1 (78.7kcalmol^?1) at the MP2/6-311G(d, p) level, 71.Okcalmol^?1 (76.3kcalmol^?1) and 70.5kcalmol^?1 (76.0kcalmol^?1) at the QCISD(T)/6-311 +G(d, p)//MP2/6-311G(d, p) level, and 66.9kcalmol^?1 (71.7kcalmol^?1) and 67.3kcalmol^?1 (72.1kcalmol¹) at the G3//B3LYP level of theory. Calculated harmonic vibrational frequencies at the B3LYP/6-31G(d) level along with transition state barrier heights from the G3//B3LYP level of theory are used to obtain RRKM reaction rate constants for each transition state, which determine the branching ratio between the two HCI elimination channels. Even at internal energies well above both HCI elimination barriers, the HCI elimination leading to propyne is strongly favoured. The smaller rate constant for the HCI elimination leading to allene can be attributed to the strong hindrance of the methyl rotor in the corresponding transition state.     

ChemInform Abstract: Characterization of the GaO4Al12(OH)24(H2O)7+ 12 Polyoxocation by MAS NMR and IR Spectroscopies and Powder X-Ray Diffraction.

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